How to Find GCF of 462/42, 938/105?

GCF of 462/42, 938/105

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 462/42, 938/105 i.e 14/210 easily. The following is the detailed procedure to determine the greatest common factor of fractions 462/42, 938/105.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 462/42,938/105?

Given fractions are 462/42,938/105

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 462/42,938/105, numerators are 462,938

Denominators are 42,105

The GCF of 462,938 is 14 .

LCM of 42,105 is 210.

The greatest common factor of 462/42,938/105 = [GCF of 462,938]/[LCM of 42,105]= 14/210

Therefore, the GCF of 462/42,938/105 is 14/210.

Greatest Common Factor of 462,938

To find the highest common factor of 462,938, we have to find the factors of both numbers and list the highest common factor.

The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462

The factors of 938 are 1, 2, 7, 14, 67, 134, 469, 938

The HCF of 462,938 is 14.

Lets's calculate GCF of 462,938

Greatest Common Factor (GCF) of 462,938 By Common Division

2	462, 938
7	231, 469
	33, 67

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 462,938 By Matching Biggest Common Factor Method

Now, list down the factors of 462

1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462

Now, list down the factors of 938

1,2,7,14,67,134,469,938

Greatest Common Factor

We found the factors 462,938 . The biggest common factor number is the GCF number.
So the greatest common factor 462,938 is 14.

Lets's calculate LCM of 42,105

Lowest Common Multiple of 42,105 using Common Division

3	42, 105
7	14, 35
	2, 5

∴ So the LCM of the given numbers is 3 x 7 x 2 x 5 = 210

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/210

Therefore, the GCF of Fractions 462/42,938/105 is 14/210

Least Common Multiple of 42,105 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 42,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,105) = 21

common factors(in case of two or more numbers have common factors) = 1

GCF(42,105) x common factors =21 x 1 = 21

LCM(42,105) = ( 42 × 105 ) / 21

LCM(42,105) = 4410 / 21

LCM(42,105) = 210

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FAQs on GCF of Fractions of 462/42, 938/105

1. What is the HCF of 462,938?

The HCF of 462,938 is 14

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 462/42, 938/105?

Answer: GCF of Numerators as per given numbers 462/42, 938/105 is

GCF of Numerators i.e. for 462,938 is 14

LCM of denominators i.e. for 42,105 is 210.

Thus, GCF of Fractions is 14/210.Finally, GCF of Fractions for 462/42, 938/105 is 14/210.